arXiv subjects

Ingo Homrighausen

Publications and source records attributed to Ingo Homrighausen.

4 recordsLinked to original sources

arXiv2019

Out of equilibrium mean field dynamics in the transverse field Ising model

We investigate the quench dynamics of the transverse field Ising model on a finite fully connected lattice as a prime example of non-equilibrium mean field dynamics. Using a rate function approach we compute the leading order corrections to the mean field behavior analytically. Our focus is threefold: i) We analyze the validity of the mean field approximation and observe that deviations can occur quickly even for large systems. ii) We study the variance of the order parameter and identify four qualitative different regions that cannot be distinguished by solely looking at its mean. iii) We derive the complete entanglement Hamiltonian for a bipartition of the lattice, which remarkably turns out to be a time-dependent harmonic oscillator within the validity of the mean field analysis.

cond-mat.stat-mech↗

arXiv2017

Anomalous dynamical phase in quantum spin chains with long-range interactions

The existence or absence of non-analytic cusps in the Loschmidt-echo return rate is traditionally employed to distinguish between a regular dynamical phase (regular cusps) and a trivial phase (no cusps) in quantum spin chains after a global quench. However, numerical evidence in a recent study [J. C. Halimeh and V. Zauner-Stauber, arXiv:1610.02019] suggests that instead of the trivial phase a distinct anomalous dynamical phase characterized by a novel type of non-analytic cusps occurs in the one-dimensional transverse-field Ising model when interactions are sufficiently long-range. Using an analytic semiclassical approach and exact diagonalization, we show that this anomalous phase also arises in the fully-connected case of infinite-range interactions, and we discuss its defining signature. Our results show that the transition from the regular to the anomalous dynamical phase coincides with Z2-symmetry breaking in the infinite-time limit, thereby showing a connection between two different concepts of dynamical criticality. Our work further expands the dynamical phase diagram of long-range interacting quantum spin chains, and can be tested experimentally in ion-trap setups and ultracold atoms in optical cavities, where interactions are inherently long-range.

cond-mat.stat-mech↗

arXiv2013

Entanglement propagation and typicality of measurements in the quantum Kac ring

We study the time evolution of entanglement in a quantum version of the Kac ring. Our model consists of two spin chains and quantum gates instead of the classical markers. The gates take one qubit from each ring at a time as an input and entangle them. Subsequently, one ring is rotated. This protocol creates non-trivial entanglement between the two rings, which we measure by the entanglement entropy. The features of the entanglement evolution can best be understood by using knowledge about the behavior of an ensemble of classical Kac rings. For instance, the recurrence time of this quantum many-body system is twice the length of the chain and "thermalization" only occurs on time scales much smaller than the dimension of the Hilbert space. The model thus elucidates the relation between distribution of measurement results in quantum and classical systems: While in classical systems repeated measurements are performed over an ensemble of systems, the corresponding result is obtained by measuring the same quantum system prepared in an appropriate superposition repeatedly.

cond-mat.stat-mech↗

arXiv2013

Fluctuation Effects in the Pair-Annihilation Process with Lévy Dynamics

We investigate the density decay in the pair-annihilation process A+A->0 in the case when the particles perform anomalous diffusion on a cubic lattice. The anomalous diffusion is realized via Lévy flights, which are characterized by long-range jumps and lead to superdiffusive behavior. As a consequence, the critical dimension depends continuously on the control parameter of the Lévy flight distribution. This instance is used to study the system close to the critical dimension by means of the nonperturbative renormalization group theory. Close to the critical dimension, the assumption of well-stirred reactants is violated by anticorrelations between the particles, and the law of mass action breaks down. The breakdown of the law of mass action is known to be caused by long-range fluctuations. We identify three interrelated consequences of these fluctuations. First, despite being a nonuniversal quantity and thus depending on the microscopic details, the renormalized reaction rate can be approximated by a universal law close to the critical dimension. The emergence of universality relies on the fact that long-range fluctuations suppress the influence of the underlying microscopic details. Second, as criticality is approached, the macroscopic reaction rate decreases such that the law of mass action loses its significance. And third, additional nonanalytic power law corrections complement the analytic law of mass action term. An increasing number of those corrections accumulate and give an essential contribution as the critical dimension is approached. We test our findings for two implementations of Lévy flights that differ in the way they cross over to the normal diffusion.

cond-mat.stat-mech↗